02341_02413_02431_03241_03412_03421_04123_04132_04213_04231_04312_04321

Counting sequence:
1, 1, 2, 6, 24, 108, 517, 2580, 13277, 69956, 375523, 2046393, 11291232, 62954575, 354139163, 2007464860, 11455640891, 65756198379, 379409903992, 2199334938209, 12802019416555, 74798669115432, 438516581229747, 2578835415720416, 15208702319342870, 89927210626144019, 533005690952120498, 3166180739828123982, 18846584060274483157, 112398367697187844181, 671523911133583255448, 4018706774817784236602, 24087326202516995486315, 144586126453184080411950, 869085401365072758359137, 5230719600455432818148141, 31520409831325553252519341, 190162372803590296056952175, 1148504895789457613160868957, 6943715945734894247920438085, 42022225778307662507192051567, 254549961137867869415255024247, 1543313984587182195685210289899, 9364931397955286156486818280632, 56873112577757474259849429633394, 345657242683256160441523582087493, 2102353851295376800979994736917069, 12795982379336775491182499776854016, 77935650654475916813024286490921993, 474986493951181041883645820199913714, 2896659886230297525360326238757884004, 17675599896983326737783387011002382768, 107919797467564943383654218940807259215, 659278404034369402375256144570834899233, 4029659479143810004063337689269488381852, 24642860213918857626042963054884352530838, 150774918311369904033493038993550563200134, 922942609305659414403245938996054208018788, 5652241089067915134982754203545572406319514, 34630614410340894113978747455988878363490834, 212269085706158308585106782487826509589516163, 1301649793565475919525595215331241991407906381, 7985029599437140963482885923599312370616507475, 49003633263685113016028288912721658990185249097, 300845882806068542909958798190140458106509300634, 1847646225168720700751816981431645597835558207588, 11351354023215109455684289878410528343251407927114, 69763134775683388384096332578847305377884511528543, 428893384267096081297890023540458676462798354843443, 2637627820200024812681423735587512954647920653954547, 16226110861507652036972294081638331308345658789450935, 99850039395081591985517276023700077525049005868749734, 614626390498457935573945513205890537477254226302470228, 3784423811368349786403939800697164233509439295629879104, 23308295278707993765657647777915790970464574810454650304, 143595278123568636075656806773326530839739787191970567905, 884882407487323846896491996871929587680797953138167284183, 5454358643383196008743948355817069249532779906991911858493, 33628820938314503810253995922391915652613661271344913823270, 207389427618298178176111622589625463979273637052957154630136, 1279280899870778167611982794105802314242359231406791686084910, 7893088232568911767281381859994847688812319920548215485792573, 48711022081116824220251565883126570273462656469846313481389338, 300679877364364820005414983441444759185021330837396334402296868, 1856419001838362890948549065888706633258109269524698669003813702, 11464098993164376868162838923309542899732968417671447587019405590, 70809898787657095912562151506390407824429122042766323859549473823, 437457694623032484421981106498902330044592625188951927355917620891, 2703112833873723165268248249333079658898166266302838695592578126972, 16706149886980374038306023634235966535191669979300187227435866632901, 103269191883714750226268195250307775580217719687925124194880132975094, 638477464345442452718004793245278476483040184685226521055018583423505, 3948198691848769253190013010292627289828681461766265817632214346324654, 24419083526873403050323380545665664246444857104431180285065431973152920, 151054966215642680427308577282128805312573807451226230509676182609972588, 934575410704762845805074306403345744606278266643890742937976173972791839, 5783168468803002299422342356188828557785273985393805554140568047371219530, 35792167059122578744034312524251008999168940887752636247767465821286202711, 221553875369234773514010834103043790518904166080166578352624582551617511022, 1371634848459576401996449642844929483087995227631430388343649238732699068351, 8493058385322437598977442154793646702489695236205455425718409438542643132745

Implicit equation for the generating function in Maple syntax:
-x*F(x)^6+x*(x+3)*F(x)^5-x*(3*x+4)*F(x)^4+2*x*(1+2*x)*F(x)^3-2*x^2*F(x)^2+(1-x)*F(x)-1 = 0

Implicit equation for the generating function in latex syntax:
-x F \! \left(x \right)^{6}+x \left(x +3\right) F \! \left(x \right)^{5}-x \left(3 x +4\right) F \! \left(x \right)^{4}+2 x \left(1+2 x \right) F \! \left(x \right)^{3}-2 x^{2} F \! \left(x \right)^{2}+\left(1-x \right) F \! \left(x \right)-1 = 0

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 108
a(6) = 517
a(7) = 2580
a(8) = 13277
a(9) = 69956
a(10) = 375523
a(11) = 2046393
a(12) = 11291232
a(13) = 62954575
a(14) = 354139163
a(15) = 2007464860
a(16) = 11455640891
a(17) = 65756198379
a(18) = 379409903992
a(19) = 2199334938209
a(20) = 12802019416555
a(21) = 74798669115432
a(22) = 438516581229747
a(23) = 2578835415720416
a(24) = 15208702319342870
a(25) = 89927210626144019
a(26) = 533005690952120498
a(27) = 3166180739828123982
a(28) = 18846584060274483157
a(29) = 112398367697187844181
a(30) = 671523911133583255448
a(31) = 4018706774817784236602
a(32) = 24087326202516995486315
a(33) = 144586126453184080411950
a(34) = 869085401365072758359137
a(35) = 5230719600455432818148141
a(36) = 31520409831325553252519341
a(37) = 190162372803590296056952175
a(38) = 1148504895789457613160868957
a(39) = 6943715945734894247920438085
a(40) = 42022225778307662507192051567
a(41) = 254549961137867869415255024247
a(42) = 1543313984587182195685210289899
a(43) = 9364931397955286156486818280632
a(44) = 56873112577757474259849429633394
a(45) = 345657242683256160441523582087493
a(46) = 2102353851295376800979994736917069
a(47) = 12795982379336775491182499776854016
a(48) = 77935650654475916813024286490921993
a(49) = 474986493951181041883645820199913714
a(50) = 2896659886230297525360326238757884004
a(51) = 17675599896983326737783387011002382768
a(52) = 107919797467564943383654218940807259215
a(53) = 659278404034369402375256144570834899233
a(54) = 4029659479143810004063337689269488381852
a(55) = 24642860213918857626042963054884352530838
a(56) = 150774918311369904033493038993550563200134
a(n+57) = -1/170*(36429503*n^5+10123667410*n^4+1125306256805*n^3+62540562021650*n^2+1737844576161512*n+19315595597188320)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+56)-1/57120*(1798780617799441669*n^5+422322403344226393235*n^4+39655417049331639232805*n^3+1861497298639784878178005*n^2+43684036873976206128730926*n+409989312613868101519055760)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+48)+1/19040*(146751103810381249*n^5+35194095111317779010*n^4+3375575757974202084215*n^3+161854337122284890125870*n^2+3879698752368006677347776*n+37192687718816715849249840)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+49)-1/19040*(24157437766684273*n^5+5905531802026906160*n^4+577356627679268872675*n^3+28217243841357158304400*n^2+689395655335258488641332*n+6735877168512407169674880)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+50)+3/3808*(115077648643469*n^5+28495025029972276*n^4+2821099083762143879*n^3+139585978246776293748*n^2+3451690782090288874492*n+34124837837691118427616)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+51)+1/1904*(10094380043275*n^5+2627468565737690*n^4+273561113348769565*n^3+14240958900222810806*n^2+370673232619048084224*n+3859219047263196299616)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+52)-1/9520*(11048636087637*n^5+2883892018243620*n^4+301092030515000555*n^3+15717373612054815120*n^2+410224565435420680588*n+4282672360040962697520)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+53)+3/4760*(3897317477*n^5+661969065250*n^4+29917714105535*n^3-598336751858150*n^2-75090905798490312*n-1438444165524413520)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+54)+1/7140*(55579306351*n^5+15172113565880*n^4+1656666951679805*n^3+90446257184215840*n^2+2468950325947482204*n+26958178791399337200)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+55)-1/19040*(7344935948635588041*n^5+1357069956476567414460*n^4+99314194648930556470835*n^3+3590387776407173586316620*n^2+63917435878706639167270924*n+446207638140435549403181760)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+41)-1/11424*(143391538030561528*n^5+77256482753703734669*n^4+10330195061184217621382*n^3+590244796162053883024471*n^2+15577385785752449393390718*n+156743202067295451889956408)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+42)+1/14280*(5645307042197447978*n^5+1216960941578987755480*n^4+104869794590526891116185*n^3+4515743860964415650454545*n^2+97167992555946819332912862*n+835856550451893143507350950)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+43)-1/11424*(6121351114203904037*n^5+1324860573732304348198*n^4+114671768150252347776547*n^3+4961536168335050085422342*n^2+107312189014333472882473212*n+928207685454030156725261640)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+44)+1/57120*(24679889108363750194*n^5+5432771223146272833905*n^4+478270882837908026885780*n^3+21047958131362307484036055*n^2+463050869305847640685364706*n+4073984264783362269255421680)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+45)-1/5712*(1385018447342771233*n^5+311112633299927101364*n^4+27948477937438829249369*n^3+1255122520608634366207924*n^2+28177375245832980781880082*n+252982450990770387940386864)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+46)+1/19040*(1894942817768331298*n^5+435090135452808023675*n^4+39953007228247215839660*n^3+1834069789403294753033965*n^2+42089852325668933537636442*n+386298571036483767822896160)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+47)-1/57120*(11275810966190104019*n^5+2190856846195136540620*n^4+167884587833785317625465*n^3+6360939061679931214313660*n^2+119416667319079082180567076*n+890056764377605586765489040)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+35)+1/9520*(3151391850559835963*n^5+595103950320060532540*n^4+44711322740308889934805*n^3+1671927257535257716867930*n^2+31135839664108476411672502*n+231130440391022009628457740)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+36)-1/1904*(700476453298091242*n^5+130251806781261518063*n^4+9659574567084048486100*n^3+357205615831775182017091*n^2+6587824056804349909828168*n+48482378178902974682544348)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+37)+1/57120*(25055180656927910492*n^5+4555520019760066368745*n^4+330037428207408065301910*n^3+11905252459187871674672375*n^2+213740180728221557205206838*n+1527128575179148558794329280)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+38)-1/57120*(30161915058115285133*n^5+5459750116319275759915*n^4+392785943648326592508685*n^3+14023103460820180614220865*n^2+248097365726798410941112002*n+1736851058316966101200870680)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+39)+1/57120*(33028307806250899492*n^5+6078170135984892569195*n^4+444412061686255894217210*n^3+16117516181691819382525945*n^2+289471790474437443720578718*n+2055200791696009176875435280)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+40)+3/19040*(457497700760811543*n^5+59708160300646452105*n^4+3119037573164034241155*n^3+81574021983602987332535*n^2+1068988488254868026820902*n+5620486413748454218532880)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+29)-1/57120*(1492905664686258644*n^5+201500502920055851965*n^4+10827561507949980553210*n^3+289234228984403728264955*n^2+3835459972348826721004746*n+20159397096171161091728040)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+30)-1/57120*(2018405104038600077*n^5+273631598689776718135*n^4+14878577093397634669585*n^3+406531071021707759801525*n^2+5597413234443645356424558*n+31171905756142306033358880)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+31)+1/28560*(3025048152504877649*n^5+457522788808283372830*n^4+27886766526384274335055*n^3+856642477594086945708230*n^2+13265967841716696904846596*n+82859085908346531414811140)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+32)-1/28560*(1976703052293726872*n^5+345169184072168603365*n^4+24189785244950100423880*n^3+849340684805344027316405*n^2+14925183963504568807656918*n+104923119378559478299852140)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+33)+1/57120*(6574002295115052656*n^5+1273365966617326864645*n^4+96958208914594028563570*n^3+3641665004036798136664235*n^2+67650174923322848656014414*n+498234480988548694813592400)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+34)+1/19040*(92875799550841931*n^5+12294864978844898290*n^4+616871440942615640345*n^3+14883731908670522895410*n^2+174055717686088643973704*n+792432298913016069160920)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+23)-1/57120*(828132306056780422*n^5+101116674595574681825*n^4+4831957773440887106480*n^3+113062148768404592275435*n^2+1294909569761799318276798*n+5797022355908741352536280)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+24)+1/19040*(419101140107127004*n^5+50791505706013626635*n^4+2429077716150675907530*n^3+57216775970988049327205*n^2+662251695245105441990386*n+3002500500546931249471080)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+25)+1/14280*(145447369685589259*n^5+18039199806025441280*n^4+922148323289259143405*n^3+24278971658023293216025*n^2+328308751574540320327911*n+1815760025610791182991910)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+26)-1/57120*(799110358748911633*n^5+118962295829055951995*n^4+6988725606355006265225*n^3+202993622243368016797405*n^2+2920179724571978594618862*n+16666511532526755187128000)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+27)-1/57120*(636900718048903262*n^5+48380805839050866625*n^4+651964361756601178720*n^3-33253970631087679922065*n^2-1104785195621814072319062*n-9327192940934375279209920)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+28)+1/19040*(73348465414571133*n^5+5873983316186517795*n^4+186357154086327066885*n^3+2922665817778207991845*n^2+22604997779450136910142*n+68750453288095272776640)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+18)-1/5712*(9766726316902699*n^5+780970896636050957*n^4+24669048245096580779*n^3+384010242225839948851*n^2+2939046723327473117682*n+8825457214570345301304)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+19)+1/9520*(44233001996729426*n^5+3609960082023220315*n^4+115486944104238819140*n^3+1796234230630787577395*n^2+13403757930070295615864*n+37429675500233154259020)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+20)-1/57120*(117056043302411999*n^5+5910216581931558310*n^4+11132478101735250265*n^3-4174189655177565382570*n^2-84850194107929601802444*n-509289128349932756875320)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+21)+1/9520*(95798411319194161*n^5+8460123475635077075*n^4+292376592196499892055*n^3+4902772116271359692375*n^2+39342199825996099800774*n+117690594242551202887740)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+22)+1/57120*(19506320672656154*n^5+1295509887342498235*n^4+34166228617473356020*n^3+446810792049345193685*n^2+2893506599369008165146*n+7408996394128520895720)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+14)-1/19040*(5798234293573643*n^5+449904551979214120*n^4+13710070819377410925*n^3+205879132649133325340*n^2+1527766032175083355132*n+4491689878711282130640)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+15)+1/57120*(63239791761031367*n^5+4421457104075934025*n^4+120913107004508963695*n^3+1603668056694134220815*n^2+10173449742158728682658*n+24043728964202608687560)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+16)-1/19040*(25166287465012813*n^5+1895732160294196850*n^4+55549915705182806095*n^3+784794285685560354250*n^2+5263951746017601532672*n+12997082407355459069640)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+17)-1/14280*(n+3)*(163759458917*n^4+3999140808064*n^3+35759941038013*n^2+138376022277866*n+195392634704280)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+4)-4/255*(n+3)*(n+2)*(n+1)*(41264566*n^2+492378809*n+1392163335)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+2)-1/57120*(105321626488373*n^5+8379700935560035*n^4+226027379163441565*n^3+2795551294006591325*n^2+16364874502918424742*n+36857921492733813720)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+9)+1/57120*(42151069746904*n^5+8084275559102195*n^4+286131378400632530*n^3+4160668705504349845*n^2+27584621698356560046*n+69283710989690638320)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+10)-1/57120*(625987084149583*n^5+49416683683968155*n^4+1427649669016888895*n^3+19572653490458350705*n^2+129600755298351587262*n+334826647990454345400)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+11)+1/57120*(1181965137196019*n^5+73490161935689125*n^4+1717266153800851015*n^3+18781227442280706095*n^2+94313729852835951546*n+164953532971978759800)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+12)-1/57120*(1642527338207713*n^5+183308518319935640*n^4+6461805057486388835*n^3+102379916226639884920*n^2+762241308395440530252*n+2177870140270111710960)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+13)+3/19040*(275620558993*n^5+8683164741110*n^4+109936565938495*n^3+689209032103810*n^2+2121777905252192*n+2555051413977120)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+5)-1/57120*(20510953891186*n^5+796930701558185*n^4+12208339786699580*n^3+91760290676249515*n^2+337755239332506774*n+486827512753805640)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+6)-1/19040*(13672278486428*n^5+686160433491055*n^4+12993775697642550*n^3+117764901650282545*n^2+515490304286908022*n+877120393864696320)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+7)-1/9520*(11905948444723*n^5+496318654712570*n^4+8377694457189115*n^3+71152983544547710*n^2+302658214512471562*n+514109679835712340)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+8)+1/1785*(n+2)*(n+3)*(9304000366*n^3+166265700750*n^2+933626654579*n+1670744516340)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+3)+2193632/255*n*(n-1)*(n+3)*(n+2)*(n+1)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n)+56/51*n*(308311*n+1528964)*(n+3)*(n+2)*(n+1)/(5*n+286)/(5*n+282)/(5*n+283)/(5*n+284)/(n+57)*a(n+1), n >= 57

Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 108
a(6) = 517
a(7) = 2580
a(8) = 13277
a(9) = 69956
a(10) = 375523
a(11) = 2046393
a(12) = 11291232
a(13) = 62954575
a(14) = 354139163
a(15) = 2007464860
a(16) = 11455640891
a(17) = 65756198379
a(18) = 379409903992
a(19) = 2199334938209
a(20) = 12802019416555
a(21) = 74798669115432
a(22) = 438516581229747
a(23) = 2578835415720416
a(24) = 15208702319342870
a(25) = 89927210626144019
a(26) = 533005690952120498
a(27) = 3166180739828123982
a(28) = 18846584060274483157
a(29) = 112398367697187844181
a(30) = 671523911133583255448
a(31) = 4018706774817784236602
a(32) = 24087326202516995486315
a(33) = 144586126453184080411950
a(34) = 869085401365072758359137
a(35) = 5230719600455432818148141
a(36) = 31520409831325553252519341
a(37) = 190162372803590296056952175
a(38) = 1148504895789457613160868957
a(39) = 6943715945734894247920438085
a(40) = 42022225778307662507192051567
a(41) = 254549961137867869415255024247
a(42) = 1543313984587182195685210289899
a(43) = 9364931397955286156486818280632
a(44) = 56873112577757474259849429633394
a(45) = 345657242683256160441523582087493
a(46) = 2102353851295376800979994736917069
a(47) = 12795982379336775491182499776854016
a(48) = 77935650654475916813024286490921993
a(49) = 474986493951181041883645820199913714
a(50) = 2896659886230297525360326238757884004
a(51) = 17675599896983326737783387011002382768
a(52) = 107919797467564943383654218940807259215
a(53) = 659278404034369402375256144570834899233
a(54) = 4029659479143810004063337689269488381852
a(55) = 24642860213918857626042963054884352530838
a(56) = 150774918311369904033493038993550563200134
a{\left(n + 57 \right)} = \frac{2193632 n \left(n - 1\right) \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) a{\left(n \right)}}{255 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{56 n \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(308311 n + 1528964\right) a{\left(n + 1 \right)}}{51 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{4 \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(41264566 n^{2} + 492378809 n + 1392163335\right) a{\left(n + 2 \right)}}{255 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(n + 2\right) \left(n + 3\right) \left(9304000366 n^{3} + 166265700750 n^{2} + 933626654579 n + 1670744516340\right) a{\left(n + 3 \right)}}{1785 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(n + 3\right) \left(163759458917 n^{4} + 3999140808064 n^{3} + 35759941038013 n^{2} + 138376022277866 n + 195392634704280\right) a{\left(n + 4 \right)}}{14280 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(36429503 n^{5} + 10123667410 n^{4} + 1125306256805 n^{3} + 62540562021650 n^{2} + 1737844576161512 n + 19315595597188320\right) a{\left(n + 56 \right)}}{170 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{3 \left(3897317477 n^{5} + 661969065250 n^{4} + 29917714105535 n^{3} - 598336751858150 n^{2} - 75090905798490312 n - 1438444165524413520\right) a{\left(n + 54 \right)}}{4760 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(55579306351 n^{5} + 15172113565880 n^{4} + 1656666951679805 n^{3} + 90446257184215840 n^{2} + 2468950325947482204 n + 26958178791399337200\right) a{\left(n + 55 \right)}}{7140 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{3 \left(275620558993 n^{5} + 8683164741110 n^{4} + 109936565938495 n^{3} + 689209032103810 n^{2} + 2121777905252192 n + 2555051413977120\right) a{\left(n + 5 \right)}}{19040 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(10094380043275 n^{5} + 2627468565737690 n^{4} + 273561113348769565 n^{3} + 14240958900222810806 n^{2} + 370673232619048084224 n + 3859219047263196299616\right) a{\left(n + 52 \right)}}{1904 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(11048636087637 n^{5} + 2883892018243620 n^{4} + 301092030515000555 n^{3} + 15717373612054815120 n^{2} + 410224565435420680588 n + 4282672360040962697520\right) a{\left(n + 53 \right)}}{9520 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(11905948444723 n^{5} + 496318654712570 n^{4} + 8377694457189115 n^{3} + 71152983544547710 n^{2} + 302658214512471562 n + 514109679835712340\right) a{\left(n + 8 \right)}}{9520 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(13672278486428 n^{5} + 686160433491055 n^{4} + 12993775697642550 n^{3} + 117764901650282545 n^{2} + 515490304286908022 n + 877120393864696320\right) a{\left(n + 7 \right)}}{19040 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(20510953891186 n^{5} + 796930701558185 n^{4} + 12208339786699580 n^{3} + 91760290676249515 n^{2} + 337755239332506774 n + 486827512753805640\right) a{\left(n + 6 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(42151069746904 n^{5} + 8084275559102195 n^{4} + 286131378400632530 n^{3} + 4160668705504349845 n^{2} + 27584621698356560046 n + 69283710989690638320\right) a{\left(n + 10 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(105321626488373 n^{5} + 8379700935560035 n^{4} + 226027379163441565 n^{3} + 2795551294006591325 n^{2} + 16364874502918424742 n + 36857921492733813720\right) a{\left(n + 9 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{3 \left(115077648643469 n^{5} + 28495025029972276 n^{4} + 2821099083762143879 n^{3} + 139585978246776293748 n^{2} + 3451690782090288874492 n + 34124837837691118427616\right) a{\left(n + 51 \right)}}{3808 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(625987084149583 n^{5} + 49416683683968155 n^{4} + 1427649669016888895 n^{3} + 19572653490458350705 n^{2} + 129600755298351587262 n + 334826647990454345400\right) a{\left(n + 11 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(1181965137196019 n^{5} + 73490161935689125 n^{4} + 1717266153800851015 n^{3} + 18781227442280706095 n^{2} + 94313729852835951546 n + 164953532971978759800\right) a{\left(n + 12 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(1642527338207713 n^{5} + 183308518319935640 n^{4} + 6461805057486388835 n^{3} + 102379916226639884920 n^{2} + 762241308395440530252 n + 2177870140270111710960\right) a{\left(n + 13 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(5798234293573643 n^{5} + 449904551979214120 n^{4} + 13710070819377410925 n^{3} + 205879132649133325340 n^{2} + 1527766032175083355132 n + 4491689878711282130640\right) a{\left(n + 15 \right)}}{19040 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(9766726316902699 n^{5} + 780970896636050957 n^{4} + 24669048245096580779 n^{3} + 384010242225839948851 n^{2} + 2939046723327473117682 n + 8825457214570345301304\right) a{\left(n + 19 \right)}}{5712 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(19506320672656154 n^{5} + 1295509887342498235 n^{4} + 34166228617473356020 n^{3} + 446810792049345193685 n^{2} + 2893506599369008165146 n + 7408996394128520895720\right) a{\left(n + 14 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(24157437766684273 n^{5} + 5905531802026906160 n^{4} + 577356627679268872675 n^{3} + 28217243841357158304400 n^{2} + 689395655335258488641332 n + 6735877168512407169674880\right) a{\left(n + 50 \right)}}{19040 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(25166287465012813 n^{5} + 1895732160294196850 n^{4} + 55549915705182806095 n^{3} + 784794285685560354250 n^{2} + 5263951746017601532672 n + 12997082407355459069640\right) a{\left(n + 17 \right)}}{19040 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(44233001996729426 n^{5} + 3609960082023220315 n^{4} + 115486944104238819140 n^{3} + 1796234230630787577395 n^{2} + 13403757930070295615864 n + 37429675500233154259020\right) a{\left(n + 20 \right)}}{9520 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(63239791761031367 n^{5} + 4421457104075934025 n^{4} + 120913107004508963695 n^{3} + 1603668056694134220815 n^{2} + 10173449742158728682658 n + 24043728964202608687560\right) a{\left(n + 16 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(73348465414571133 n^{5} + 5873983316186517795 n^{4} + 186357154086327066885 n^{3} + 2922665817778207991845 n^{2} + 22604997779450136910142 n + 68750453288095272776640\right) a{\left(n + 18 \right)}}{19040 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(92875799550841931 n^{5} + 12294864978844898290 n^{4} + 616871440942615640345 n^{3} + 14883731908670522895410 n^{2} + 174055717686088643973704 n + 792432298913016069160920\right) a{\left(n + 23 \right)}}{19040 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(95798411319194161 n^{5} + 8460123475635077075 n^{4} + 292376592196499892055 n^{3} + 4902772116271359692375 n^{2} + 39342199825996099800774 n + 117690594242551202887740\right) a{\left(n + 22 \right)}}{9520 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(117056043302411999 n^{5} + 5910216581931558310 n^{4} + 11132478101735250265 n^{3} - 4174189655177565382570 n^{2} - 84850194107929601802444 n - 509289128349932756875320\right) a{\left(n + 21 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(143391538030561528 n^{5} + 77256482753703734669 n^{4} + 10330195061184217621382 n^{3} + 590244796162053883024471 n^{2} + 15577385785752449393390718 n + 156743202067295451889956408\right) a{\left(n + 42 \right)}}{11424 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(145447369685589259 n^{5} + 18039199806025441280 n^{4} + 922148323289259143405 n^{3} + 24278971658023293216025 n^{2} + 328308751574540320327911 n + 1815760025610791182991910\right) a{\left(n + 26 \right)}}{14280 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(146751103810381249 n^{5} + 35194095111317779010 n^{4} + 3375575757974202084215 n^{3} + 161854337122284890125870 n^{2} + 3879698752368006677347776 n + 37192687718816715849249840\right) a{\left(n + 49 \right)}}{19040 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(419101140107127004 n^{5} + 50791505706013626635 n^{4} + 2429077716150675907530 n^{3} + 57216775970988049327205 n^{2} + 662251695245105441990386 n + 3002500500546931249471080\right) a{\left(n + 25 \right)}}{19040 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{3 \left(457497700760811543 n^{5} + 59708160300646452105 n^{4} + 3119037573164034241155 n^{3} + 81574021983602987332535 n^{2} + 1068988488254868026820902 n + 5620486413748454218532880\right) a{\left(n + 29 \right)}}{19040 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(636900718048903262 n^{5} + 48380805839050866625 n^{4} + 651964361756601178720 n^{3} - 33253970631087679922065 n^{2} - 1104785195621814072319062 n - 9327192940934375279209920\right) a{\left(n + 28 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(700476453298091242 n^{5} + 130251806781261518063 n^{4} + 9659574567084048486100 n^{3} + 357205615831775182017091 n^{2} + 6587824056804349909828168 n + 48482378178902974682544348\right) a{\left(n + 37 \right)}}{1904 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(799110358748911633 n^{5} + 118962295829055951995 n^{4} + 6988725606355006265225 n^{3} + 202993622243368016797405 n^{2} + 2920179724571978594618862 n + 16666511532526755187128000\right) a{\left(n + 27 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(828132306056780422 n^{5} + 101116674595574681825 n^{4} + 4831957773440887106480 n^{3} + 113062148768404592275435 n^{2} + 1294909569761799318276798 n + 5797022355908741352536280\right) a{\left(n + 24 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(1385018447342771233 n^{5} + 311112633299927101364 n^{4} + 27948477937438829249369 n^{3} + 1255122520608634366207924 n^{2} + 28177375245832980781880082 n + 252982450990770387940386864\right) a{\left(n + 46 \right)}}{5712 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(1492905664686258644 n^{5} + 201500502920055851965 n^{4} + 10827561507949980553210 n^{3} + 289234228984403728264955 n^{2} + 3835459972348826721004746 n + 20159397096171161091728040\right) a{\left(n + 30 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(1798780617799441669 n^{5} + 422322403344226393235 n^{4} + 39655417049331639232805 n^{3} + 1861497298639784878178005 n^{2} + 43684036873976206128730926 n + 409989312613868101519055760\right) a{\left(n + 48 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(1894942817768331298 n^{5} + 435090135452808023675 n^{4} + 39953007228247215839660 n^{3} + 1834069789403294753033965 n^{2} + 42089852325668933537636442 n + 386298571036483767822896160\right) a{\left(n + 47 \right)}}{19040 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(1976703052293726872 n^{5} + 345169184072168603365 n^{4} + 24189785244950100423880 n^{3} + 849340684805344027316405 n^{2} + 14925183963504568807656918 n + 104923119378559478299852140\right) a{\left(n + 33 \right)}}{28560 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(2018405104038600077 n^{5} + 273631598689776718135 n^{4} + 14878577093397634669585 n^{3} + 406531071021707759801525 n^{2} + 5597413234443645356424558 n + 31171905756142306033358880\right) a{\left(n + 31 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(3025048152504877649 n^{5} + 457522788808283372830 n^{4} + 27886766526384274335055 n^{3} + 856642477594086945708230 n^{2} + 13265967841716696904846596 n + 82859085908346531414811140\right) a{\left(n + 32 \right)}}{28560 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(3151391850559835963 n^{5} + 595103950320060532540 n^{4} + 44711322740308889934805 n^{3} + 1671927257535257716867930 n^{2} + 31135839664108476411672502 n + 231130440391022009628457740\right) a{\left(n + 36 \right)}}{9520 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(5645307042197447978 n^{5} + 1216960941578987755480 n^{4} + 104869794590526891116185 n^{3} + 4515743860964415650454545 n^{2} + 97167992555946819332912862 n + 835856550451893143507350950\right) a{\left(n + 43 \right)}}{14280 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(6121351114203904037 n^{5} + 1324860573732304348198 n^{4} + 114671768150252347776547 n^{3} + 4961536168335050085422342 n^{2} + 107312189014333472882473212 n + 928207685454030156725261640\right) a{\left(n + 44 \right)}}{11424 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(6574002295115052656 n^{5} + 1273365966617326864645 n^{4} + 96958208914594028563570 n^{3} + 3641665004036798136664235 n^{2} + 67650174923322848656014414 n + 498234480988548694813592400\right) a{\left(n + 34 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(7344935948635588041 n^{5} + 1357069956476567414460 n^{4} + 99314194648930556470835 n^{3} + 3590387776407173586316620 n^{2} + 63917435878706639167270924 n + 446207638140435549403181760\right) a{\left(n + 41 \right)}}{19040 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(11275810966190104019 n^{5} + 2190856846195136540620 n^{4} + 167884587833785317625465 n^{3} + 6360939061679931214313660 n^{2} + 119416667319079082180567076 n + 890056764377605586765489040\right) a{\left(n + 35 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(24679889108363750194 n^{5} + 5432771223146272833905 n^{4} + 478270882837908026885780 n^{3} + 21047958131362307484036055 n^{2} + 463050869305847640685364706 n + 4073984264783362269255421680\right) a{\left(n + 45 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(25055180656927910492 n^{5} + 4555520019760066368745 n^{4} + 330037428207408065301910 n^{3} + 11905252459187871674672375 n^{2} + 213740180728221557205206838 n + 1527128575179148558794329280\right) a{\left(n + 38 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} - \frac{\left(30161915058115285133 n^{5} + 5459750116319275759915 n^{4} + 392785943648326592508685 n^{3} + 14023103460820180614220865 n^{2} + 248097365726798410941112002 n + 1736851058316966101200870680\right) a{\left(n + 39 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)} + \frac{\left(33028307806250899492 n^{5} + 6078170135984892569195 n^{4} + 444412061686255894217210 n^{3} + 16117516181691819382525945 n^{2} + 289471790474437443720578718 n + 2055200791696009176875435280\right) a{\left(n + 40 \right)}}{57120 \left(n + 57\right) \left(5 n + 282\right) \left(5 n + 283\right) \left(5 n + 284\right) \left(5 n + 286\right)}, \quad n \geq 57

Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/24734/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[16,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[16,x]*F[8,x]
F[8,x] = F[48,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[16,x]
F[11,x] = F[12,x]+F[20,x]
F[12,x] = F[13,x]+F[17,x]
F[13,x] = F[14,x]*F[4,x]
F[14,x] = 1/F[16,x]*F[15,x]
F[15,x] = F[2,x]
F[16,x] = x
F[17,x] = F[18,x]
F[18,x] = F[0,x]*F[14,x]*F[16,x]*F[19,x]
F[19,x] = F[4,x]+F[9,x]
F[20,x] = F[21,x]
F[21,x] = F[16,x]*F[22,x]*F[30,x]
F[22,x] = F[23,x]+F[4,x]
F[23,x] = -F[26,x]+F[24,x]
F[24,x] = 1/F[16,x]*F[25,x]
F[25,x] = F[6,x]
F[26,x] = F[27,x]
F[27,x] = F[16,x]*F[28,x]
F[28,x] = 1/F[16,x]*F[29,x]
F[29,x] = F[9,x]
F[30,x] = -F[47,x]+F[31,x]
F[31,x] = 1/F[16,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]+F[42,x]
F[34,x] = F[35,x]
F[35,x] = F[16,x]*F[36,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[0,x]*F[4,x]
F[38,x] = F[39,x]
F[39,x] = F[0,x]*F[16,x]*F[4,x]*F[40,x]
F[40,x] = 1/F[16,x]*F[41,x]
F[41,x] = F[2,x]
F[42,x] = F[43,x]
F[43,x] = F[16,x]*F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[14,x]*F[16,x]*F[46,x]
F[46,x] = F[0,x]+F[34,x]
F[47,x] = F[44,x]
F[48,x] = F[49,x]
F[49,x] = F[0,x]*F[16,x]*F[19,x]*F[40,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{16}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{48}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{20}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{17}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{0}\! \left(x \right) F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right) F_{22}\! \left(x \right) F_{30}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{6}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{16}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{9}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{42}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{16}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{2}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{16}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{0}\! \left(x \right)+F_{34}\! \left(x \right)
F_{47}\! \left(x \right) = F_{44}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{40}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_16(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_16(x)*F_8(x))
Eq(F_8(x), F_48(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_16(x))
Eq(F_11(x), F_12(x) + F_20(x))
Eq(F_12(x), F_13(x) + F_17(x))
Eq(F_13(x), F_14(x)*F_4(x))
Eq(F_14(x), F_15(x)/F_16(x))
Eq(F_15(x), F_2(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_0(x)*F_14(x)*F_16(x)*F_19(x))
Eq(F_19(x), F_4(x) + F_9(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_16(x)*F_22(x)*F_30(x))
Eq(F_22(x), F_23(x) + F_4(x))
Eq(F_23(x), F_24(x) - F_26(x))
Eq(F_24(x), F_25(x)/F_16(x))
Eq(F_25(x), F_6(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_16(x)*F_28(x))
Eq(F_28(x), F_29(x)/F_16(x))
Eq(F_29(x), F_9(x))
Eq(F_30(x), F_31(x) - F_47(x))
Eq(F_31(x), F_32(x)/F_16(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x) + F_42(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_16(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_0(x)*F_4(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_0(x)*F_16(x)*F_4(x)*F_40(x))
Eq(F_40(x), F_41(x)/F_16(x))
Eq(F_41(x), F_2(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_16(x)*F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_14(x)*F_16(x)*F_46(x))
Eq(F_46(x), F_0(x) + F_34(x))
Eq(F_47(x), F_44(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_0(x)*F_16(x)*F_19(x)*F_40(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], 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"pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 2], [1, 1], [1, 2], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 2], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 2]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 2], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}

Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24765/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[16,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[16,x]*F[8,x]
F[8,x] = F[47,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[16,x]
F[11,x] = F[12,x]+F[20,x]
F[12,x] = F[13,x]+F[17,x]
F[13,x] = F[14,x]*F[4,x]
F[14,x] = 1/F[16,x]*F[15,x]
F[15,x] = F[2,x]
F[16,x] = x
F[17,x] = F[18,x]
F[18,x] = F[0,x]*F[14,x]*F[16,x]*F[19,x]
F[19,x] = F[4,x]+F[9,x]
F[20,x] = F[21,x]
F[21,x] = F[16,x]*F[22,x]*F[30,x]
F[22,x] = F[23,x]+F[4,x]
F[23,x] = -F[26,x]+F[24,x]
F[24,x] = 1/F[16,x]*F[25,x]
F[25,x] = F[6,x]
F[26,x] = F[27,x]
F[27,x] = F[16,x]*F[28,x]
F[28,x] = 1/F[16,x]*F[29,x]
F[29,x] = F[9,x]
F[30,x] = -F[45,x]+F[31,x]
F[31,x] = 1/F[16,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]+F[42,x]
F[34,x] = F[35,x]
F[35,x] = F[16,x]*F[36,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[0,x]*F[4,x]
F[38,x] = F[39,x]
F[39,x] = F[0,x]*F[16,x]*F[4,x]*F[40,x]
F[40,x] = 1/F[16,x]*F[41,x]
F[41,x] = F[2,x]
F[42,x] = F[43,x]
F[43,x] = F[16,x]*F[2,x]*F[44,x]
F[44,x] = F[0,x]+F[34,x]
F[45,x] = F[46,x]
F[46,x] = F[14,x]*F[16,x]*F[44,x]
F[47,x] = F[48,x]
F[48,x] = F[0,x]*F[16,x]*F[19,x]*F[40,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{16}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{47}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{20}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{17}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{0}\! \left(x \right) F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right) F_{22}\! \left(x \right) F_{30}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{6}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{16}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{9}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{42}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{16}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{2}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{16}\! \left(x \right) F_{2}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{0}\! \left(x \right)+F_{34}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{40}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_16(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_16(x)*F_8(x))
Eq(F_8(x), F_47(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_16(x))
Eq(F_11(x), F_12(x) + F_20(x))
Eq(F_12(x), F_13(x) + F_17(x))
Eq(F_13(x), F_14(x)*F_4(x))
Eq(F_14(x), F_15(x)/F_16(x))
Eq(F_15(x), F_2(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_0(x)*F_14(x)*F_16(x)*F_19(x))
Eq(F_19(x), F_4(x) + F_9(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_16(x)*F_22(x)*F_30(x))
Eq(F_22(x), F_23(x) + F_4(x))
Eq(F_23(x), F_24(x) - F_26(x))
Eq(F_24(x), F_25(x)/F_16(x))
Eq(F_25(x), F_6(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_16(x)*F_28(x))
Eq(F_28(x), F_29(x)/F_16(x))
Eq(F_29(x), F_9(x))
Eq(F_30(x), F_31(x) - F_45(x))
Eq(F_31(x), F_32(x)/F_16(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x) + F_42(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_16(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_0(x)*F_4(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_0(x)*F_16(x)*F_4(x)*F_40(x))
Eq(F_40(x), F_41(x)/F_16(x))
Eq(F_41(x), F_2(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_16(x)*F_2(x)*F_44(x))
Eq(F_44(x), F_0(x) + F_34(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_14(x)*F_16(x)*F_44(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_0(x)*F_16(x)*F_19(x)*F_40(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 1, 2, 3], [0, 4, 1, 3, 2], [0, 4, 2, 1, 3], [0, 4, 2, 3, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 1, 2, 3], [0, 4, 1, 3, 2], [0, 4, 2, 1, 3], [0, 4, 2, 3, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], 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[[1, 1], [1, 1], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 1], [1, 1], [1, 2], [1, 2], [1, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 2], [1, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 2], [1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 1], [1, 2], [1, 1], [1, 2], [1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 2], [1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 2], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 2]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[1, 1], [1, 2], [1, 1], [1, 2], [1, 2]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 1], [1, 2], [1, 1], [1, 2], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 1], [1, 2], [1, 1], [1, 2], [1, 2]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 2], [1, 1], [1, 2], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 2], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 2]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 2], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}

Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25230/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[16,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[16,x]*F[8,x]
F[8,x] = F[48,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[16,x]
F[11,x] = F[12,x]+F[20,x]
F[12,x] = F[13,x]+F[17,x]
F[13,x] = F[14,x]*F[4,x]
F[14,x] = 1/F[16,x]*F[15,x]
F[15,x] = F[2,x]
F[16,x] = x
F[17,x] = F[18,x]
F[18,x] = F[0,x]*F[14,x]*F[16,x]*F[19,x]
F[19,x] = F[4,x]+F[9,x]
F[20,x] = F[21,x]
F[21,x] = F[16,x]*F[22,x]*F[30,x]
F[22,x] = F[23,x]+F[4,x]
F[23,x] = -F[26,x]+F[24,x]
F[24,x] = 1/F[16,x]*F[25,x]
F[25,x] = F[6,x]
F[26,x] = F[27,x]
F[27,x] = F[16,x]*F[28,x]
F[28,x] = 1/F[16,x]*F[29,x]
F[29,x] = F[9,x]
F[30,x] = -F[47,x]+F[31,x]
F[31,x] = 1/F[16,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]+F[42,x]
F[34,x] = F[35,x]
F[35,x] = F[16,x]*F[36,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[0,x]*F[4,x]
F[38,x] = F[39,x]
F[39,x] = F[0,x]*F[16,x]*F[4,x]*F[40,x]
F[40,x] = 1/F[16,x]*F[41,x]
F[41,x] = F[2,x]
F[42,x] = F[43,x]
F[43,x] = F[16,x]*F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[14,x]*F[16,x]*F[46,x]
F[46,x] = F[0,x]+F[34,x]
F[47,x] = F[44,x]
F[48,x] = F[49,x]
F[49,x] = F[0,x]*F[16,x]*F[19,x]*F[40,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{16}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{48}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{20}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{17}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{0}\! \left(x \right) F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right) F_{22}\! \left(x \right) F_{30}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{6}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{16}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{9}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{42}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{16}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{2}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{16}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{0}\! \left(x \right)+F_{34}\! \left(x \right)
F_{47}\! \left(x \right) = F_{44}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{40}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_16(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_16(x)*F_8(x))
Eq(F_8(x), F_48(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_16(x))
Eq(F_11(x), F_12(x) + F_20(x))
Eq(F_12(x), F_13(x) + F_17(x))
Eq(F_13(x), F_14(x)*F_4(x))
Eq(F_14(x), F_15(x)/F_16(x))
Eq(F_15(x), F_2(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_0(x)*F_14(x)*F_16(x)*F_19(x))
Eq(F_19(x), F_4(x) + F_9(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_16(x)*F_22(x)*F_30(x))
Eq(F_22(x), F_23(x) + F_4(x))
Eq(F_23(x), F_24(x) - F_26(x))
Eq(F_24(x), F_25(x)/F_16(x))
Eq(F_25(x), F_6(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_16(x)*F_28(x))
Eq(F_28(x), F_29(x)/F_16(x))
Eq(F_29(x), F_9(x))
Eq(F_30(x), F_31(x) - F_47(x))
Eq(F_31(x), F_32(x)/F_16(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x) + F_42(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_16(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_0(x)*F_4(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_0(x)*F_16(x)*F_4(x)*F_40(x))
Eq(F_40(x), F_41(x)/F_16(x))
Eq(F_41(x), F_2(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_16(x)*F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_14(x)*F_16(x)*F_46(x))
Eq(F_46(x), F_0(x) + F_34(x))
Eq(F_47(x), F_44(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_0(x)*F_16(x)*F_19(x)*F_40(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 1, 2, 3], [0, 4, 1, 3, 2], [0, 4, 2, 1, 3], [0, 4, 2, 3, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 1, 2, 3], [0, 4, 1, 3, 2], [0, 4, 2, 1, 3], [0, 4, 2, 3, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
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"requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 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[1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 2], [1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 1], [1, 2], [1, 1], [1, 2], [1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 2], [1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 2], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 2]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[1, 1], [1, 2], [1, 1], [1, 2], [1, 2]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 1], [1, 2], [1, 1], [1, 2], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 1], [1, 2], [1, 1], [1, 2], [1, 2]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 2], [1, 1], [1, 2], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 2], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 2]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 2], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}

Specification 4
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25527/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[16,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[16,x]*F[8,x]
F[8,x] = F[48,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[16,x]
F[11,x] = F[12,x]+F[20,x]
F[12,x] = F[13,x]+F[17,x]
F[13,x] = F[14,x]*F[4,x]
F[14,x] = 1/F[16,x]*F[15,x]
F[15,x] = F[2,x]
F[16,x] = x
F[17,x] = F[18,x]
F[18,x] = F[0,x]*F[14,x]*F[16,x]*F[19,x]
F[19,x] = F[4,x]+F[9,x]
F[20,x] = F[21,x]
F[21,x] = F[16,x]*F[22,x]*F[30,x]
F[22,x] = F[23,x]+F[4,x]
F[23,x] = -F[26,x]+F[24,x]
F[24,x] = 1/F[16,x]*F[25,x]
F[25,x] = F[6,x]
F[26,x] = F[27,x]
F[27,x] = F[16,x]*F[28,x]
F[28,x] = 1/F[16,x]*F[29,x]
F[29,x] = F[9,x]
F[30,x] = -F[47,x]+F[31,x]
F[31,x] = 1/F[16,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]+F[42,x]
F[34,x] = F[35,x]
F[35,x] = F[16,x]*F[36,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[0,x]*F[4,x]
F[38,x] = F[39,x]
F[39,x] = F[0,x]*F[16,x]*F[4,x]*F[40,x]
F[40,x] = 1/F[16,x]*F[41,x]
F[41,x] = F[2,x]
F[42,x] = F[43,x]
F[43,x] = F[16,x]*F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[14,x]*F[16,x]*F[46,x]
F[46,x] = F[0,x]+F[34,x]
F[47,x] = F[44,x]
F[48,x] = F[49,x]
F[49,x] = F[0,x]*F[16,x]*F[19,x]*F[40,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{16}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{48}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{20}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{17}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{0}\! \left(x \right) F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right) F_{22}\! \left(x \right) F_{30}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{6}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{16}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{9}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{42}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{16}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{2}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{16}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{0}\! \left(x \right)+F_{34}\! \left(x \right)
F_{47}\! \left(x \right) = F_{44}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{40}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_16(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_16(x)*F_8(x))
Eq(F_8(x), F_48(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_16(x))
Eq(F_11(x), F_12(x) + F_20(x))
Eq(F_12(x), F_13(x) + F_17(x))
Eq(F_13(x), F_14(x)*F_4(x))
Eq(F_14(x), F_15(x)/F_16(x))
Eq(F_15(x), F_2(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_0(x)*F_14(x)*F_16(x)*F_19(x))
Eq(F_19(x), F_4(x) + F_9(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_16(x)*F_22(x)*F_30(x))
Eq(F_22(x), F_23(x) + F_4(x))
Eq(F_23(x), F_24(x) - F_26(x))
Eq(F_24(x), F_25(x)/F_16(x))
Eq(F_25(x), F_6(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_16(x)*F_28(x))
Eq(F_28(x), F_29(x)/F_16(x))
Eq(F_29(x), F_9(x))
Eq(F_30(x), F_31(x) - F_47(x))
Eq(F_31(x), F_32(x)/F_16(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x) + F_42(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_16(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_0(x)*F_4(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_0(x)*F_16(x)*F_4(x)*F_40(x))
Eq(F_40(x), F_41(x)/F_16(x))
Eq(F_41(x), F_2(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_16(x)*F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_14(x)*F_16(x)*F_46(x))
Eq(F_46(x), F_0(x) + F_34(x))
Eq(F_47(x), F_44(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_0(x)*F_16(x)*F_19(x)*F_40(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 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[1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 2], [1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 1], [1, 2], [1, 1], [1, 2], [1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 2], [1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 2], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 2]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[1, 1], [1, 2], [1, 1], [1, 2], [1, 2]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 1], [1, 2], [1, 1], [1, 2], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 1], [1, 2], [1, 1], [1, 2], [1, 2]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 2]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 2], [1, 1], [1, 2], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 2], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 2]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 6], [0, 6], [0, 6], [0, 6], [0, 6]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 2], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 2], [1, 2], [1, 2], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}

Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25885/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[16,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[16,x]*F[8,x]
F[8,x] = F[47,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[16,x]
F[11,x] = F[12,x]+F[20,x]
F[12,x] = F[13,x]+F[17,x]
F[13,x] = F[14,x]*F[4,x]
F[14,x] = 1/F[16,x]*F[15,x]
F[15,x] = F[2,x]
F[16,x] = x
F[17,x] = F[18,x]
F[18,x] = F[0,x]*F[14,x]*F[16,x]*F[19,x]
F[19,x] = F[4,x]+F[9,x]
F[20,x] = F[21,x]
F[21,x] = F[16,x]*F[22,x]*F[30,x]
F[22,x] = F[23,x]+F[4,x]
F[23,x] = -F[26,x]+F[24,x]
F[24,x] = 1/F[16,x]*F[25,x]
F[25,x] = F[6,x]
F[26,x] = F[27,x]
F[27,x] = F[16,x]*F[28,x]
F[28,x] = 1/F[16,x]*F[29,x]
F[29,x] = F[9,x]
F[30,x] = -F[45,x]+F[31,x]
F[31,x] = 1/F[16,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]+F[42,x]
F[34,x] = F[35,x]
F[35,x] = F[16,x]*F[36,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[0,x]*F[4,x]
F[38,x] = F[39,x]
F[39,x] = F[0,x]*F[16,x]*F[4,x]*F[40,x]
F[40,x] = 1/F[16,x]*F[41,x]
F[41,x] = F[2,x]
F[42,x] = F[43,x]
F[43,x] = F[16,x]*F[2,x]*F[44,x]
F[44,x] = F[0,x]+F[34,x]
F[45,x] = F[46,x]
F[46,x] = F[14,x]*F[16,x]*F[44,x]
F[47,x] = F[48,x]
F[48,x] = F[0,x]*F[16,x]*F[19,x]*F[40,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{16}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{47}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{20}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{17}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{0}\! \left(x \right) F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right) F_{22}\! \left(x \right) F_{30}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{6}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{16}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{9}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{42}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{16}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{2}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{16}\! \left(x \right) F_{2}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{0}\! \left(x \right)+F_{34}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{14}\! \left(x \right) F_{16}\! \left(x \right) F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{19}\! \left(x \right) F_{40}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_16(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_16(x)*F_8(x))
Eq(F_8(x), F_47(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_16(x))
Eq(F_11(x), F_12(x) + F_20(x))
Eq(F_12(x), F_13(x) + F_17(x))
Eq(F_13(x), F_14(x)*F_4(x))
Eq(F_14(x), F_15(x)/F_16(x))
Eq(F_15(x), F_2(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_0(x)*F_14(x)*F_16(x)*F_19(x))
Eq(F_19(x), F_4(x) + F_9(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_16(x)*F_22(x)*F_30(x))
Eq(F_22(x), F_23(x) + F_4(x))
Eq(F_23(x), F_24(x) - F_26(x))
Eq(F_24(x), F_25(x)/F_16(x))
Eq(F_25(x), F_6(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_16(x)*F_28(x))
Eq(F_28(x), F_29(x)/F_16(x))
Eq(F_29(x), F_9(x))
Eq(F_30(x), F_31(x) - F_45(x))
Eq(F_31(x), F_32(x)/F_16(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x) + F_42(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_16(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_0(x)*F_4(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_0(x)*F_16(x)*F_4(x)*F_40(x))
Eq(F_40(x), F_41(x)/F_16(x))
Eq(F_41(x), F_2(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_16(x)*F_2(x)*F_44(x))
Eq(F_44(x), F_0(x) + F_34(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_14(x)*F_16(x)*F_44(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_0(x)*F_16(x)*F_19(x)*F_40(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 1, 2, 3], [0, 4, 1, 3, 2], [0, 4, 2, 1, 3], [0, 4, 2, 3, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [0, 4, 1, 2, 3], [0, 4, 1, 3, 2], [0, 4, 2, 1, 3], [0, 4, 2, 3, 1], [0, 4, 3, 1, 2], [0, 4, 3, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
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